Conference description

This is a conference on Model Theory from a philosophical perspective. The conference is supported by the University Paris Ouest Nanterre (Ireph and EA 373) and by the Agence Nationale de la Recherche (Logiscience program, supervised by P. Wagner at the Institute of History and Philosophy of Science and Technology). It will be held in Paris from June 2 to June 5 2010 at the University Paris Ouest (June 2 and June 3) and at the Ecole Normale Supérieure (June 4 and June 5). Conference organizers are Denis Bonnay, Brice Halimi and Jean-Michel Salanskis.

Model theory seems to have reached its zenith in the sixties and the seventies, when it was seen by many as virtually identical to mathematical logic. The works of Gödel and Cohen on the continuum hypothesis, though falling only indirectly within the domain of model theory, did bring to it some reflected glory. The works of Montague or Putnam bear witness to the profound impact of model theory, both on analytical philosophy and on the foundations of scientific linguistics.

Thirty or forty years later, the situation has decidedly changed, as other perspectives have all but replaced model theory, as for example in the areas of analytical philosophy and scientific linguistics mentioned above. Still, model theory has retained its function as a standard reference language for a wide variety of perspectives, fields and problems. At the same time, as a branch of mathematical logic, it has given rise to a number of important developments.

The aim of the conference is to take stock of the current situation, viewing it from a variety of perspectives, of which the following are but possible examples:

1) History. Model theory now has a history, associated to a large extent with Tarski, who blazed the trail leading from the invention of logical semantics, in his famous 1935 paper, to the active promotion of what he himself called model theory. We would welcome any discussions shedding light on that evolution, as well as reflections on the avenues that have been opened up in the field beyond the pioneering work done by Tarski himself.

2) Technicalities. Over the course of its brief history, model theory (and logical semantics) have seen a number of significant innovations. The possible variation of interpretation structures for a given theory has been studied within the context of set theory, and model theory has intersected with a number of set theoretic themes (large cardinals, descriptive set theory, and so on). The fundamental core of model theory has been thought of as open to modifications, in particular so as to match category theory. As to logical semantics, different notions of model have been defined so as to allow for completeness theorems corresponding to different logics. Cogent discussions of these and related issues are also solicited.

3) Applications. Model theory and logical semantics have also been used as a kind of rational pattern and as a guide for scientific study in other areas. We invite talks having to do with all such applications of model theory -- in linguistics, cognitive science, economics, etc.

4) Philosophy. Finally, model theory and logical semantics, as Popper reports he discovered them,have been viewed as the most exact means with which to account for the fundamental philosophical problem of knowledge. Indeed, they have been thought to provide the most general and the most comprehensive way to describe what it is for a discourse to say the truth about reality. For that reason, numerous philosophical studies have come to depend on model theory. This is the case with the philosophy of mathematics, and a similar development may be seen in the way in which general epistemology has been molded, and also in the way questions in metaphysics, esthetics and general philosophy have been dealt with. Talks exploring such issues would be most welcome.

To conclude this tentative anticipation of some of the themes and questions that will be addressed, it seems to us that our work will be all the more relevant and fruitful if we keep in mind the distinction between logical semantics (let's say, the theory of truth as Tarski developed it around 1935) and model theory properly speaking which, in the realm of ZFC, studies the "degrees of freedom" that theories and their interpretation structures permit each other.